Ultrasound Matrix Imaging—Part II: The Distortion Matrix for Aberration Correction Over Multiple Isoplanatic Patches

This is the second article in a series of two which report on a matrix approach for ultrasound imaging in heterogeneous media. This article describes the quantification and correction of aberration, i.e. the distortion of an image caused by spatial variations in the medium speed-of-sound. Adaptive focusing can compensate for aberration, but is only effective over a restricted area called the isoplanatic patch. Here, we use an experimentally-recorded matrix of reflected acoustic signals to synthesize a set of virtual transducers. We then examine wave propagation between these virtual transducers and an arbitrary correction plane. Such wave-fronts consist of two components: (i) An ideal geometric wave-front linked to diffraction and the input focusing point, and; (ii) Phase distortions induced by the speed-of-sound variations. These distortions are stored in a so-called distortion matrix, the singular value decomposition of which gives access to an optimized focusing law at any point. We show that, by decoupling the aberrations undergone by the outgoing and incoming waves and applying an iterative strategy, compensation for even high-order and spatially-distributed aberrations can be achieved. After a numerical validation of the process, ultrasound matrix imaging (UMI) is applied to the in-vivo imaging of a gallbladder. A map of isoplanatic modes is retrieved and is shown to be strongly correlated with the arrangement of tissues constituting the medium. The corresponding focusing laws yield an ultrasound image with drastically improved contrast and transverse resolution. UMI thus provides a flexible and powerful route towards computational ultrasound.

I. Introduction

In most ultrasound imaging, the human body is insonified by a series of incident waves. The medium reflectivity is then estimated by detecting acoustic backscatter from short-scale variations of the acoustic impedance. An image (spatial map) of reflectivity is commonly constructed using delay-and-sum beamforming (DAS). In this process, echoes coming from a particular point, or image pixel, are selected by summing the signals generated by this echo at the aperture, thereby accounting – for each element – for the respective time-of-flight associated with the forward and return travel paths of the ultrasonic wave between the probe and that point. The resulting signal is allocated at the corresponding pixel of the image, and the procedure repeated for each pixel. The time-of-flight between any incident wave and focal point is calculated with the assumption that the medium is homogeneous with a constant speed-of-sound. However, in human tissue, long-scale fluctuations of the acoustic impedance can invalidate this assumption [1]. The resulting incorrectly calculated times-of-flight (also called focusing laws) can lead to aberration of the associated image, meaning that resolution and contrast are strongly degraded. While adaptive focusing methods have been developed to deal with this issue, they rely on the hypothesis that the speed-of-sound variations occur only in a thin screen at the probe aperture. However, this assumption is simply incorrect in soft tissues [2] such as fat, skin and muscle, in which the order of magnitude of acoustic impedance fluctuations is around 5% [3]. This causes higher-order aberrations which are only invariant over small regions, often referred to as isoplanatic patches. To tackle this issue, recent studies [4], [5] extract an aberration law for each image voxel by probing the correlation of the time-delayed echoes coming from adjacent focal spots. The aberration laws are estimated either in the time domain [4], [6], [7], [8] or in the Fourier domain [5], [9], for different insonification sequences (focused beams [6], [8], single-transducer insonification [5] or plane wave illumination [4]). In all of these techniques, a focusing law is estimated in either the receive [6], [9] or transmit [5], [7] mode, but this law is then used to compensate for aberrations in both reflection and transmission. However, spatial reciprocity between input and output is only valid if the emission and detection of waves are performed in the same basis; in other words, the distortion undergone by a wavefront travelling to and from a particular point is only the same if the wave has interacted with the same heterogeneities in both directions. If this condition is not fulfilled, applying the same aberration phase law in transmit and receive modes may improve the image quality to some degree, but will not be optimal.